D. V. Lytkina, A. Kh. Zhurtov, “Finite groups whose maximal subgroups have only soluble proper subgroups”, Sib. Èlektron. Mat. Izv., 2022, Volume 19, Issue 1,Pages <nobr>237

Mathematical logic, algebra and number theory

Finite groups whose maximal subgroups have only soluble proper subgroups

D. V. Lytkina^abc, A. Kh. Zhurtov^d

^a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
^b Novosibirsk State University, 2, Pirogova str., Novosibirsk, 630090, Russia
^c Siberian State University of telecommunications and information sciences, 86, Kirova str., Novosibirsk, 630102, Russia
^d Kabardin-Balkarian State University, 173, Chernyshevskogo str., Nalchik, 360004, Russia

Abstract: We give a description of a finite group whose maximal subgroups possess only soluble proper subgroups, which implies the answer to the well-known question on composition factors of finite groups, whose second maximal subgroups are soluble.

Keywords: finite group, maximal subgroup, solubility.

UDC: 512.542

MSC: 20F16

Received March 7, 2022, published April 8, 2022

Language: English

DOI: 10.33048/semi.2022.19.017